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Let $AB = 6$, $BC = 8$, and $AC = 10$. What is the area of the circumcircle of $\triangle ABC$ minus the area of the incircle of $\triangle ABC$?

eileenthecoolbean  Jul 14, 2017
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 The radius of the cicumscribing circle is given by :

 

[ Product of the side lengrhs ]  /  [ 4 * Area of the triangle ]  =

 

[ 6 * 8 * 10 ] / [ 4 (1/2) * 6 * 8]  =    10 / 2  =  5 units

 

The radius of the incircle is given by 

 

[ 2*Area of the triangle] / [Perimeter]  = [ 2* (1/2) * 6 * 8] / [ 6 + 8 + 10]  = 48 / 24  = 2 units

 

So....the area of the circumcircle - area of the incircle  =

 

[pi] [5^2 - 2^2] =  pi * [25 - 4] = 21pi  units^2 ≈ 65.97 units^2

 

 

cool cool cool

CPhill  Jul 14, 2017

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